Game design equation (Two variables(multiple two variables) and one Result (for every case)) how to make the...
$begingroup$
I tried to solve this using multiple methods but i couldn't figure it out.
i don't know what to use in order to solve this
basically i have an input x and x2
Heading
when x = 1 and x2 = 1 Y = 45
when x = 1 and x2 = -1 Y = 315
when x = -1 and x2 = 1 Y = 135
when x = -1 and x2 = -1 Y = 225
when x = 0 and x2 = 1 Y = 90
when x = 0 and x2 = -1 Y = 270
when x = 1 and x2 = 0 Y = 360
when x = -1 and x2 = 0 Y = 180
To explain it more i want an equation that when ever i input x ,x2 values in it i get the same y value.
Ii don't know if its feasible or if math can deal with that type of situation but i believe that somehow there should be a way to make that equation
I tried to use Excel to solve this as a regression but it didn't work
analysis regression
asked Jan 20 at 8:25
Dia EidDia Eid
102
$endgroup$
add a comment |
$begingroup$
I tried to solve this using multiple methods but i couldn't figure it out.
i don't know what to use in order to solve this
basically i have an input x and x2
Heading
when x = 1 and x2 = 1 Y = 45
when x = 1 and x2 = -1 Y = 315
when x = -1 and x2 = 1 Y = 135
when x = -1 and x2 = -1 Y = 225
when x = 0 and x2 = 1 Y = 90
when x = 0 and x2 = -1 Y = 270
when x = 1 and x2 = 0 Y = 360
when x = -1 and x2 = 0 Y = 180
To explain it more i want an equation that when ever i input x ,x2 values in it i get the same y value.
Ii don't know if its feasible or if math can deal with that type of situation but i believe that somehow there should be a way to make that equation
I tried to use Excel to solve this as a regression but it didn't work
analysis regression
asked Jan 20 at 8:25
Dia EidDia Eid
102
$endgroup$
$begingroup$
If this is for game design, maybe just manually code a function with an if statement to find these values for you? If there is an element of continuity, then can you graph what that would look like?
$endgroup$
– stuart stevenson
Jan 20 at 8:32
$begingroup$
Thanks but i don't want to code it i coded it all ready i want to know if our knowledge in math can be powerful enough to create something in one line rather than coding it in 20 or so, plus i want to know because i face problems like these a lot of times and i end up coding a solution for a problem that could have been solved mathematically
$endgroup$
– Dia Eid
Jan 20 at 8:36
add a comment |
$begingroup$
I tried to solve this using multiple methods but i couldn't figure it out.
i don't know what to use in order to solve this
basically i have an input x and x2
Heading
when x = 1 and x2 = 1 Y = 45
when x = 1 and x2 = -1 Y = 315
when x = -1 and x2 = 1 Y = 135
when x = -1 and x2 = -1 Y = 225
when x = 0 and x2 = 1 Y = 90
when x = 0 and x2 = -1 Y = 270
when x = 1 and x2 = 0 Y = 360
when x = -1 and x2 = 0 Y = 180
To explain it more i want an equation that when ever i input x ,x2 values in it i get the same y value.
Ii don't know if its feasible or if math can deal with that type of situation but i believe that somehow there should be a way to make that equation
I tried to use Excel to solve this as a regression but it didn't work
analysis regression
asked Jan 20 at 8:25
Dia EidDia Eid
102
$endgroup$
I tried to solve this using multiple methods but i couldn't figure it out.
i don't know what to use in order to solve this
basically i have an input x and x2
Heading
when x = 1 and x2 = 1 Y = 45
when x = 1 and x2 = -1 Y = 315
when x = -1 and x2 = 1 Y = 135
when x = -1 and x2 = -1 Y = 225
when x = 0 and x2 = 1 Y = 90
when x = 0 and x2 = -1 Y = 270
when x = 1 and x2 = 0 Y = 360
when x = -1 and x2 = 0 Y = 180
To explain it more i want an equation that when ever i input x ,x2 values in it i get the same y value.
Ii don't know if its feasible or if math can deal with that type of situation but i believe that somehow there should be a way to make that equation
I tried to use Excel to solve this as a regression but it didn't work
analysis regression
analysis regression
asked Jan 20 at 8:25
Dia EidDia Eid
102
asked Jan 20 at 8:25
Dia EidDia Eid
102
asked Jan 20 at 8:25
Dia EidDia Eid
102
asked Jan 20 at 8:25
Dia EidDia Eid
102
asked Jan 20 at 8:25
Dia EidDia Eid
102
102
$begingroup$
If this is for game design, maybe just manually code a function with an if statement to find these values for you? If there is an element of continuity, then can you graph what that would look like?
$endgroup$
– stuart stevenson
Jan 20 at 8:32
$begingroup$
Thanks but i don't want to code it i coded it all ready i want to know if our knowledge in math can be powerful enough to create something in one line rather than coding it in 20 or so, plus i want to know because i face problems like these a lot of times and i end up coding a solution for a problem that could have been solved mathematically
$endgroup$
– Dia Eid
Jan 20 at 8:36
add a comment |
$begingroup$
If this is for game design, maybe just manually code a function with an if statement to find these values for you? If there is an element of continuity, then can you graph what that would look like?
$endgroup$
– stuart stevenson
Jan 20 at 8:32
$begingroup$
Thanks but i don't want to code it i coded it all ready i want to know if our knowledge in math can be powerful enough to create something in one line rather than coding it in 20 or so, plus i want to know because i face problems like these a lot of times and i end up coding a solution for a problem that could have been solved mathematically
$endgroup$
– Dia Eid
Jan 20 at 8:36
$begingroup$
If this is for game design, maybe just manually code a function with an if statement to find these values for you? If there is an element of continuity, then can you graph what that would look like?
$endgroup$
– stuart stevenson
Jan 20 at 8:32
$begingroup$
If this is for game design, maybe just manually code a function with an if statement to find these values for you? If there is an element of continuity, then can you graph what that would look like?
$endgroup$
– stuart stevenson
Jan 20 at 8:32
$begingroup$
Thanks but i don't want to code it i coded it all ready i want to know if our knowledge in math can be powerful enough to create something in one line rather than coding it in 20 or so, plus i want to know because i face problems like these a lot of times and i end up coding a solution for a problem that could have been solved mathematically
$endgroup$
– Dia Eid
Jan 20 at 8:36
$begingroup$
Thanks but i don't want to code it i coded it all ready i want to know if our knowledge in math can be powerful enough to create something in one line rather than coding it in 20 or so, plus i want to know because i face problems like these a lot of times and i end up coding a solution for a problem that could have been solved mathematically
$endgroup$
– Dia Eid
Jan 20 at 8:36
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
First of all, if you are asking how to find an angle given 2 coordinates, in vast majority of languages, there is a function atan2(y,x) (or with similar name) that allows you to pass coordinates and get the value of the angle:
$$
Y=frac{180}{pi}mathop{mathrm{atan2}}(x_2,x_1).
$$
If we insist we want integer number from $1$ to $360$, we can add modulus shift:
$$
Y = mathrm{rem}left(left[frac{180}{pi}mathop{mathrm{atan2}}(x_2,x_1)-1right], 360right)+1.
$$
In C it would be translated as ((int)round(180/PI*atan2(x2,x1)-1) % 360)+1
If we do not want trigonometric function for suchsimple problem and also do not want to use precalculated array, we can go like this.
You can represent your data in a table $A_{ij}$, where $i,j=-1,0,1$:
$$
A=45 left(
begin{array}{ccc}
5 & 4 & 3 \
6 & cdot & 2 \
7 & 8 & 1 \
end{array}
right)
$$
All numbers except 8 can be represented as a bilinear interpolation of the corners:
$$
Y'=4-2x_2-x_1x_2,qquad A'=left(
begin{array}{ccc}
5 & 4 & 3 \
6 & cdot & 2 \
7 & 4 & 1 \
end{array}
right)
$$
Now we need to add 4 to the bottom 4 to get 8. We can do it with the trick $2 (x_1+1) left(1-x_2^2right)$. Finally:
$$
Y=45left(4-2x_2-x_1x_2+2 (x_1+1) left(1-x_2^2right)right)
$$
answered Jan 20 at 10:46
Vasily MitchVasily Mitch
2,3141311
$endgroup$
$begingroup$
Sir i want first to thank you very much, then to ask you what should i learn in order to know the information that you used, you made something seemed impossible possible i never though that math can do something like that. can you please lead me to a book or topic or anything that i can start with.
$endgroup$
– Dia Eid
Jan 20 at 13:44
add a comment |
$begingroup$
There is no easy formula that gets all results in one equation, but the code can be made significantly easier than 8 cases as presented in the question. Pseudocode:
if (x==0)
{m=8, d=2}
else
{m=6+2*x, d=x}
Y=45*((m+d*x2) % 8)
The $%$-operator is the calculating the remainder of the term $m+d*x2$ modulo 8.
This will give $0$ instead if $360$ for $x=1, x2=0$, but I assume that this is OK as the design seems to be based on angles (I assume for movement).
answered Jan 20 at 10:47
IngixIngix
4,267149
$endgroup$
add a comment |
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2 Answers
2
active
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2 Answers
2
active
oldest
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active
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votes
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oldest
votes
$begingroup$
First of all, if you are asking how to find an angle given 2 coordinates, in vast majority of languages, there is a function atan2(y,x) (or with similar name) that allows you to pass coordinates and get the value of the angle:
$$
Y=frac{180}{pi}mathop{mathrm{atan2}}(x_2,x_1).
$$
If we insist we want integer number from $1$ to $360$, we can add modulus shift:
$$
Y = mathrm{rem}left(left[frac{180}{pi}mathop{mathrm{atan2}}(x_2,x_1)-1right], 360right)+1.
$$
In C it would be translated as ((int)round(180/PI*atan2(x2,x1)-1) % 360)+1
If we do not want trigonometric function for suchsimple problem and also do not want to use precalculated array, we can go like this.
You can represent your data in a table $A_{ij}$, where $i,j=-1,0,1$:
$$
A=45 left(
begin{array}{ccc}
5 & 4 & 3 \
6 & cdot & 2 \
7 & 8 & 1 \
end{array}
right)
$$
All numbers except 8 can be represented as a bilinear interpolation of the corners:
$$
Y'=4-2x_2-x_1x_2,qquad A'=left(
begin{array}{ccc}
5 & 4 & 3 \
6 & cdot & 2 \
7 & 4 & 1 \
end{array}
right)
$$
Now we need to add 4 to the bottom 4 to get 8. We can do it with the trick $2 (x_1+1) left(1-x_2^2right)$. Finally:
$$
Y=45left(4-2x_2-x_1x_2+2 (x_1+1) left(1-x_2^2right)right)
$$
answered Jan 20 at 10:46
Vasily MitchVasily Mitch
2,3141311
$endgroup$
$begingroup$
Sir i want first to thank you very much, then to ask you what should i learn in order to know the information that you used, you made something seemed impossible possible i never though that math can do something like that. can you please lead me to a book or topic or anything that i can start with.
$endgroup$
– Dia Eid
Jan 20 at 13:44
add a comment |
$begingroup$
First of all, if you are asking how to find an angle given 2 coordinates, in vast majority of languages, there is a function atan2(y,x) (or with similar name) that allows you to pass coordinates and get the value of the angle:
$$
Y=frac{180}{pi}mathop{mathrm{atan2}}(x_2,x_1).
$$
If we insist we want integer number from $1$ to $360$, we can add modulus shift:
$$
Y = mathrm{rem}left(left[frac{180}{pi}mathop{mathrm{atan2}}(x_2,x_1)-1right], 360right)+1.
$$
In C it would be translated as ((int)round(180/PI*atan2(x2,x1)-1) % 360)+1
If we do not want trigonometric function for suchsimple problem and also do not want to use precalculated array, we can go like this.
You can represent your data in a table $A_{ij}$, where $i,j=-1,0,1$:
$$
A=45 left(
begin{array}{ccc}
5 & 4 & 3 \
6 & cdot & 2 \
7 & 8 & 1 \
end{array}
right)
$$
All numbers except 8 can be represented as a bilinear interpolation of the corners:
$$
Y'=4-2x_2-x_1x_2,qquad A'=left(
begin{array}{ccc}
5 & 4 & 3 \
6 & cdot & 2 \
7 & 4 & 1 \
end{array}
right)
$$
Now we need to add 4 to the bottom 4 to get 8. We can do it with the trick $2 (x_1+1) left(1-x_2^2right)$. Finally:
$$
Y=45left(4-2x_2-x_1x_2+2 (x_1+1) left(1-x_2^2right)right)
$$
answered Jan 20 at 10:46
Vasily MitchVasily Mitch
2,3141311
$endgroup$
$begingroup$
Sir i want first to thank you very much, then to ask you what should i learn in order to know the information that you used, you made something seemed impossible possible i never though that math can do something like that. can you please lead me to a book or topic or anything that i can start with.
$endgroup$
– Dia Eid
Jan 20 at 13:44
add a comment |
$begingroup$
First of all, if you are asking how to find an angle given 2 coordinates, in vast majority of languages, there is a function atan2(y,x) (or with similar name) that allows you to pass coordinates and get the value of the angle:
$$
Y=frac{180}{pi}mathop{mathrm{atan2}}(x_2,x_1).
$$
If we insist we want integer number from $1$ to $360$, we can add modulus shift:
$$
Y = mathrm{rem}left(left[frac{180}{pi}mathop{mathrm{atan2}}(x_2,x_1)-1right], 360right)+1.
$$
In C it would be translated as ((int)round(180/PI*atan2(x2,x1)-1) % 360)+1
If we do not want trigonometric function for suchsimple problem and also do not want to use precalculated array, we can go like this.
You can represent your data in a table $A_{ij}$, where $i,j=-1,0,1$:
$$
A=45 left(
begin{array}{ccc}
5 & 4 & 3 \
6 & cdot & 2 \
7 & 8 & 1 \
end{array}
right)
$$
All numbers except 8 can be represented as a bilinear interpolation of the corners:
$$
Y'=4-2x_2-x_1x_2,qquad A'=left(
begin{array}{ccc}
5 & 4 & 3 \
6 & cdot & 2 \
7 & 4 & 1 \
end{array}
right)
$$
Now we need to add 4 to the bottom 4 to get 8. We can do it with the trick $2 (x_1+1) left(1-x_2^2right)$. Finally:
$$
Y=45left(4-2x_2-x_1x_2+2 (x_1+1) left(1-x_2^2right)right)
$$
answered Jan 20 at 10:46
Vasily MitchVasily Mitch
2,3141311
$endgroup$
First of all, if you are asking how to find an angle given 2 coordinates, in vast majority of languages, there is a function atan2(y,x) (or with similar name) that allows you to pass coordinates and get the value of the angle:
$$
Y=frac{180}{pi}mathop{mathrm{atan2}}(x_2,x_1).
$$
If we insist we want integer number from $1$ to $360$, we can add modulus shift:
$$
Y = mathrm{rem}left(left[frac{180}{pi}mathop{mathrm{atan2}}(x_2,x_1)-1right], 360right)+1.
$$
In C it would be translated as ((int)round(180/PI*atan2(x2,x1)-1) % 360)+1
If we do not want trigonometric function for suchsimple problem and also do not want to use precalculated array, we can go like this.
You can represent your data in a table $A_{ij}$, where $i,j=-1,0,1$:
$$
A=45 left(
begin{array}{ccc}
5 & 4 & 3 \
6 & cdot & 2 \
7 & 8 & 1 \
end{array}
right)
$$
All numbers except 8 can be represented as a bilinear interpolation of the corners:
$$
Y'=4-2x_2-x_1x_2,qquad A'=left(
begin{array}{ccc}
5 & 4 & 3 \
6 & cdot & 2 \
7 & 4 & 1 \
end{array}
right)
$$
Now we need to add 4 to the bottom 4 to get 8. We can do it with the trick $2 (x_1+1) left(1-x_2^2right)$. Finally:
$$
Y=45left(4-2x_2-x_1x_2+2 (x_1+1) left(1-x_2^2right)right)
$$
answered Jan 20 at 10:46
Vasily MitchVasily Mitch
2,3141311
answered Jan 20 at 10:46
Vasily MitchVasily Mitch
2,3141311
answered Jan 20 at 10:46
Vasily MitchVasily Mitch
2,3141311
answered Jan 20 at 10:46
Vasily MitchVasily Mitch
2,3141311
2,3141311
$begingroup$
Sir i want first to thank you very much, then to ask you what should i learn in order to know the information that you used, you made something seemed impossible possible i never though that math can do something like that. can you please lead me to a book or topic or anything that i can start with.
$endgroup$
– Dia Eid
Jan 20 at 13:44
add a comment |
$begingroup$
Sir i want first to thank you very much, then to ask you what should i learn in order to know the information that you used, you made something seemed impossible possible i never though that math can do something like that. can you please lead me to a book or topic or anything that i can start with.
$endgroup$
– Dia Eid
Jan 20 at 13:44
$begingroup$
Sir i want first to thank you very much, then to ask you what should i learn in order to know the information that you used, you made something seemed impossible possible i never though that math can do something like that. can you please lead me to a book or topic or anything that i can start with.
$endgroup$
– Dia Eid
Jan 20 at 13:44
$begingroup$
Sir i want first to thank you very much, then to ask you what should i learn in order to know the information that you used, you made something seemed impossible possible i never though that math can do something like that. can you please lead me to a book or topic or anything that i can start with.
$endgroup$
– Dia Eid
Jan 20 at 13:44
add a comment |
$begingroup$
There is no easy formula that gets all results in one equation, but the code can be made significantly easier than 8 cases as presented in the question. Pseudocode:
if (x==0)
{m=8, d=2}
else
{m=6+2*x, d=x}
Y=45*((m+d*x2) % 8)
The $%$-operator is the calculating the remainder of the term $m+d*x2$ modulo 8.
This will give $0$ instead if $360$ for $x=1, x2=0$, but I assume that this is OK as the design seems to be based on angles (I assume for movement).
answered Jan 20 at 10:47
IngixIngix
4,267149
$endgroup$
add a comment |
$begingroup$
There is no easy formula that gets all results in one equation, but the code can be made significantly easier than 8 cases as presented in the question. Pseudocode:
if (x==0)
{m=8, d=2}
else
{m=6+2*x, d=x}
Y=45*((m+d*x2) % 8)
The $%$-operator is the calculating the remainder of the term $m+d*x2$ modulo 8.
This will give $0$ instead if $360$ for $x=1, x2=0$, but I assume that this is OK as the design seems to be based on angles (I assume for movement).
answered Jan 20 at 10:47
IngixIngix
4,267149
$endgroup$
add a comment |
$begingroup$
There is no easy formula that gets all results in one equation, but the code can be made significantly easier than 8 cases as presented in the question. Pseudocode:
if (x==0)
{m=8, d=2}
else
{m=6+2*x, d=x}
Y=45*((m+d*x2) % 8)
The $%$-operator is the calculating the remainder of the term $m+d*x2$ modulo 8.
This will give $0$ instead if $360$ for $x=1, x2=0$, but I assume that this is OK as the design seems to be based on angles (I assume for movement).
answered Jan 20 at 10:47
IngixIngix
4,267149
$endgroup$
There is no easy formula that gets all results in one equation, but the code can be made significantly easier than 8 cases as presented in the question. Pseudocode:
if (x==0)
{m=8, d=2}
else
{m=6+2*x, d=x}
Y=45*((m+d*x2) % 8)
The $%$-operator is the calculating the remainder of the term $m+d*x2$ modulo 8.
This will give $0$ instead if $360$ for $x=1, x2=0$, but I assume that this is OK as the design seems to be based on angles (I assume for movement).
answered Jan 20 at 10:47
IngixIngix
4,267149
answered Jan 20 at 10:47
IngixIngix
4,267149
answered Jan 20 at 10:47
IngixIngix
4,267149
answered Jan 20 at 10:47
IngixIngix
4,267149
4,267149
add a comment |
add a comment |
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$begingroup$
If this is for game design, maybe just manually code a function with an if statement to find these values for you? If there is an element of continuity, then can you graph what that would look like?
$endgroup$
– stuart stevenson
Jan 20 at 8:32
$begingroup$
Thanks but i don't want to code it i coded it all ready i want to know if our knowledge in math can be powerful enough to create something in one line rather than coding it in 20 or so, plus i want to know because i face problems like these a lot of times and i end up coding a solution for a problem that could have been solved mathematically
$endgroup$
– Dia Eid
Jan 20 at 8:36